using the graph concepts for a case where I frequently add or remove
edges I came across an inconsistency:
removing an edge may invalidate the edge counter because it does not
check whether the edge existed or not. This is the code from the header
file boost/graph/adjacency_matrix.hpp:

template <typename D, typename VP, typename EP, typename GP, typename A>
 void
 remove_edge(typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor
u,
             typename adjacency_matrix<D,VP,EP,GP,A>::vertex_descriptor
v,
             adjacency_matrix<D,VP,EP,GP,A>& g)
{
   --(g.m_num_edges);
   detail::set_edge_exists(g.get_edge(u,v), false, 0);
}